An Empirical Analysis of Mobile Voice and SMS service: A

Structural Model∗

Youngsoo Kim1, Rahul Telang2, William B. Vogt3, Ramayya Krishnan4

1,2,4H. J. Heinz III College, Carnegie Mellon University,3RAND Corporation

yskimx@gmail.com, rtelang@andrew.cmu.edu, william.b.vogt@gmail.com, rk2x@andrew.cmu.edu

August 14, 2009

Abstract

In addition to wireless telephony boom, a similar exponential increasing trend in wireless dataservice -for example, short message service (SMS) – is visible as technology advances. We developa structural model to examine user demand for voice and SMS services. Specifically, we measurethe own- and the cross-price elasticities of these services. The cross-price elasticity is of significantimportance because marketing activities are critically influenced by whether the goods are substitutesor complements. The research context poses significant econometric challenges due to three-parttariffs, and sequential discrete plan choice and continuous quantity choice decisions. Using detailedindividual consumption data of more than 6000 customers, we find that SMS and voice services aresmall substitutes. A 10% increase in the price of voice minutes will induce about 0.8% increase inthe demand for SMS. The own price elasticity of voice is also low, to the order of approximately -0.1.Younger users’ demand is far more inelastic than that of older users. We then conduct counterfactualpolicy experiments that fully capture the effects of change in key parameters on the firm revenues.Finally, we discuss the generalizability of our framework.

Keywords: Wireless communication, Price elasticity, Short Message Service (SMS), StructuralModel, nonlinear tariff, substitutes vs complements, policy experiments.

∗Authors thank the seminar participants at New York University, University of Texas, Dallas and the Internationalconference of Information Systems (ICIS 2007) for valuable comments. Rahul Telang Acknowledges a generous support ofthe National Science Foundation through the CAREER award CNS-0540009. The authors also thank Atip Asvanund forhelp in data collection and tabulation. We thank Ed Barr for editorial help.

1

1 Introduction

In most countries, mobile (cellular) telephones have grown to be a central part of the telecommunicationnetwork – mobile penetration rates exceed fixed line penetration rates in all regions of the world, andby a margin of three to four times in some regions.1 Along with the growth of mobile telephony, theuse of wireless data services - specifically Short Message Service (SMS) - has also grown exponentially.The growth of mobile services has been even more spectacular in some of the less developed countriesin Africa, Asia, and Europe. Many users are giving up their traditional land lines and relying solely ontheir cellular phones as a primary communication device. A recent McKinsey study finds that mobileservices have generated billions of dollars in consumer welfare (Enriquez et al. 2007). Currently, revenuesfrom mobile data services are about 15-20% of Average Revenues per User (ARPU). 2 However, goingforward it is expected that the mobile data will become a key revenue source for mobile operators. Mostcellular operators are betting on an increasing uptake of mobile data services and investing billions ininfrastructure. Despite tremendous growth in mobile voice and data services, our understanding of howusers consume these services is still limited. In particular, little work exists that examines the interactionbetween voice and data services. In this paper, using a rich panel dataset, we estimate demand elasticitiesfor these services with a particular focus on the cross-price effects of voice and SMS.

This study has important implications for practitioners and academicians. Wireless communicationtariffs tend to be highly nonlinear being composed of a fixed fee component and a marginal fee compo-nent. While these price schemes are intuitive to describe, an empirical estimation of demand parametersunder a nonlinear price structure is non-trivial. In particular, from an academic perspective one has tocarefully model user choices for both the service plan and then subsequent consumptions. For managers,understanding user response to a typical nonlinear pricing scheme is important because it allows them tooptimally price their products. For example, a manager might want to know how changes in the fixed feeor the marginal price would impact her firm profitability. Similarly, the cross-price elasticity between twoservices has important implications for optimal pricing and promotion decisions. For example, if man-agers comprehend how voice and SMS interact (whether SMS is a substitute or a complement to voice),they can better predict the direct and indirect impact of pricing and promotion and set appropriatemarketing strategies.

However, impact of SMS on voice (and vice-versa) is ambiguous. On the one hand, SMS can be a closesubstitute of voice if it is perceived to serve the same purpose. In that case, a price increase in voice maylead to increased usage of SMS (and vice-versa). However, SMS and voice serve may possibly differentpurposes and at best they are weak substitutes. Andersson et al. (2006) argue that SMS and voice mayeven exhibit a complementary relationship. For example, a price decrease in SMS may lead to moreincoming messages for a user, who in turn may respond by increasing voice consumption. Given theseconjectures, how voice and SMS interact is an open empirical question. However, except for a coupleof recent papers which we describe in detail in the next section, the literature examining this mutualrelationship is sparse, presumably due to the lack of individual-level consumption data or relatively recentnature of this phenomenon. Our study fills this gap in the literature. We have access to individual-levelconsumption data for these services, which allows us to build a richer model and draw useful conclusions.

1http://www.itu.int/ITU-D/ict/statistics/ict/index.html2http://www.comms-dealer.com/mobile-zone/latest-news/global-revenues-non-voice-services-hits-1887bn-2008; most of

the non-voice revenues is from SMS.

2

Besides the unique data set, our paper also makes important methodological contributions. As noted,the telecom tariffs (especially in the wireless industry) tend to be two-part (or three-part) nonlinear tariffswhich require careful modeling to avoid bias in demand estimations. In our case, we not only have athree-part tariff structure with consumers’ sequential decisions (first choosing a plan and then choosingthe consumption level), we also deal with a two goods problem - voice and SMS. In this paper, we offera structural model by specifying a utility function and deriving the demand curves for these services.This model allows us to jointly specify the sequential consumption decision at an individual user levelfor these goods, and allows us to estimate the own and the cross-price elasticities for these services. Toour knowledge, this is the first study that offers a methodology to estimate the own and the cross-priceelasticities for voice and SMS services based on a detailed individual-level consumption data. Anotheradvantage of the structural model is that it allows us to perform some policy experiments. Thus, withour estimates, we can simulate and specify how changes in key strategic variables (e.g., fixed fee, marginalprice etc.) would affect the firm demand and revenues (or profitability).

Our paper is composed of two parts. In the first part, we specify a utility structure and develop ageneral model of individual consumption behavior in voice and SMS. In the second part, we estimateour model using a real world data set, explicitly allowing for the cross-effects and endogeneity in thechoice of plans and consumption levels. Our framework incorporates four crucial elements that couldaffect users’ optimal consumption behavior: (1) interrelationship of voice and SMS in demand throughthe cross-price elasticities, (2) estimation of the own-price elasticities, (3) the service-specific satiationpoints, and (4) potential for endogeneity through covariance between the voice and SMS satiation points.The fourth point is critical. If users who consume large numbers of voice minutes are also likely to sendlarge numbers of SMS, the demand for the two services would be positively correlated even if the twoservices are not complementary.

The rest of the paper is organized as follows. We provide a background on the relevant literature insection 1.1. Our research context (data and pricing scheme) is provided and analyzed in section 2. Weoutline our analytic model in section 3 and estimation strategy in section 4. In the subsequent section,we discuss our results along with the policy experiments. Finally, we conclude with a summary of ourfindings, limitation, and suggestions for future research.

1.1 Relevant Literature

The telecommunication demand modeling literature has a rich history (see Taylor 1994 for a summary).Generally, the telecommunication pricing and consumption behavior has been an intriguing researcharea because the industry has unique characteristics such as high fixed costs, low short-run marginalcosts, and network externalities. These issues pose interesting econometric challenges. More importantly,the telecommunication industry traditionally has been a regulated industry and much work has beenconducted to examine the impact of regulatory changes on user demand and social welfare.

The relevant telecommunication literature for our study can be classified into two research topics:(1) evaluating the fixed-line telecommunication demand structure, and (2) evaluating the mobile com-munication demand. Many studies have estimated price elasticity of demand in various contexts for thefixed line telephony. Taylor and Kridel (1990) make a distinction between telephone access and telephone

3

use while calculating the price elasticity of telephone demand. Distinguishing the use-based (metered)and the flat-rate pricing, some researchers investigate how users choose one over the other and how theirdemand changes under these pricing regimes (Kling and Ploeg 1990; Park et al. 1983). Miravete (2002)explicitly incorporates users’ uncertainty in the number of minutes demanded in the next month whenchoosing a plan today. Most of the studies find a low price elasticities for local voice services. Kling andPloeg (1990) estimate the elasticity to be on the order of -0.17 while Park et al.’s (1983) estimate is about-0.1.

In the domain of wireless telephony, one main research stream has been to examine the penetrationof mobile services and how the mobile communication interacts with the fixed line communication (Ahnand Lee 1999; Hausman 1999; Rodini et al. 2003; Sung and Lee 2002). The results have been conflicting.Some have found a substitution effect between the fixed lines and mobiles (Ahn and Lee 1999) whileothers have found a complementary effect (Gruber and Verboven 2001). More recently, Economides etal. (2008) report that the fixed line usage (in both local and regional services) for a household is greaterif the household owns a cellular phone and suggest that the cellular service proxies for the intensity ofhousehold communication needs.

Another research stream has analyzed market structure, mark-ups and competition between mobileproviders. Hausman (1999) estimates the welfare impact of diffusion of cellular phones. Garbacz andThompson (2007) estimate demand for mobile services in developing countries. Miravete and Roller (2004)develop a model of competition between the US cellular operators and recover key cost parameters fromaggregate demand data. Gruber (2001) analyzes how competition affects diffusion of mobile services.

Much of the previous work analyzing mobile communication is focused only on the mobile voice service,leaving out the data service such as SMS. For example, Iyengar (2004) uses individual-level data similarto ours to estimate consumer demand but he does not have information on SMS usage. Given SMS’s wideuse, the interaction of voice and SMS provides an interesting and understudied area. Recently, two papershave looked at the interaction between voice and SMS. Andersson et al. (2006) analyze relationship ofthe two services in context of network size. They estimate the cross-price elasticity of voice and SMS andshow that, depending on the network size, the relationship could be either substitutive or complementary.However, their data is highly aggregate. They use quarterly average SMS sent in Norway and use thedata over 33 quarters to estimate a reduced form model. Such a high level of aggregation precludes themfrom modeling and interpreting user behavior at a micro-level. In a recent paper, Grzybowski and Periera(2008) show that SMS and voice have a complementary relationship. While their data is at individual-level, they do not observe the user’s plan choice and hence do not observe the marginal prices paid by theuser (or even the average price paid by the user). This again forces data aggregation. Our data is richerin this regard as we can observe plan characteristics and consumers’ sequential choices (plan choice andconsumption) in detail. This allows us to build a more realistic model of the consumer decision making.

Our work is also closely related to the “multiple category purchasing behavior” line of research inmarketing discipline. Researchers have begun to understand cross-category relationships in consumers’decision-making, using multi-category models (see Seetharaman et al. 2005 for a review of this topic). Therecognition of cross-category dependencies implies that a consumer’s purchase decisions across categoriesare not independent. In other words, a consumer’s decision of whether or how much to buy in onecategory depends on her corresponding decision in the related category (Chiang 1991; Niraj et al. 2005;

4

Seetharaman et al. 2005; Song and Chintagunta 2007). In our setting, voice and SMS are two suchcategories which impact the consumption decisions of each other.

We now provide some details on our data and outline key econometric challenges.

2 Research context

2.1 Data

We collected detailed consumption data on 6847 subscribers of a cellular service provider in an Asiancountry (the operator was the third largest in the county with more than 2 million consumers at thattime) from April 2002 through December 2002. The firm offers two kinds of communication services:voice and SMS.3 We have the following consumption information at an individual level: (1) the voiceservice use measured in the number of minutes for each consumer for each month, (2) the number ofSMS’s sent for each month, and (3) demographic information about the users (gender, age, and maritalstatus). Users select into five different three-part tariffs offered by the firm. The plan is selected at thebeginning of a month. Table 1 shows the pricing scheme offered – the pricing scheme did not changeduring our research period.

Plan # Fixed fee (units)∗ Free minutes Overtime charge of Charge ofvoice service SMS service

1 350 350

3 units/min 3 units/message2 800 5173 1100 9174 1500 12175 2000 2117

∗In currency units of the country

Table 1: Pricing Scheme (Three-part nonlinear Tariff)

In Table 2, we offer descriptive statistics of our sample. In particular, we show the consumptionstatistics of voice and SMS across demographic characteristics and across five plans. The statisticsindicate that Plan 1 is heavily subscribed to. The user consumption seems to follow a reasonable pattern.The consumption of both voice and SMS is fairly heterogenous. Younger users consumer higher volumesof voice minutes as well as of SMS. Across the plans, as one moves from plan 1 to plan 5, the consumptionof both voice and SMS increases (except for the last plan when the consumption of SMS decreases). Recallfrom Table 1 that the free minutes available increase as one moves from plan 1 to plan 5.

3Due to the disclosure agreement, name of the firm is not disclosed. The available data were from about 10,000 subscribersfor the whole 2002 year. However, the first three months of the data were for trial period. About a third of the consumershad signed for a “family plan” which was not specific to an individual. So we dropped those observations. Some observationswere dropped when we did not have good demographic information on users. We also dropped those months of data whenthe users used fewer than 10 minutes of voice. This led to a final sample of about 6847 consumers for a total of 59866observations.

5

Whole SampleMean S.D. Min Max N

Voice 281.3 252.6 10.1 11845.359866SMS 11.8 34.2 0 3106

Users with Age<30Voice 329.8 299.5 10.2 11845.3

22483SMS 16.7 36.7 0 1558

30 ≤Age<40Voice 265.0965 223.455 10.08 6602.36

29520SMS 9.232893 33.69502 0 3106

Age≥40Voice 203.6786 168.1059 10.05 2916.9

7863SMS 7.315656 26.84394 0 1079

FemaleVoice 287.1297 257.9581 10.08 11845.31

32592SMS 13.19011 31.63919 0 1558

MaleVoice 274.3871 246.0002 10.05 6602.36

27274SMS 10.14611 37.10299 0 3106

Plan 1Voice 248.9897 167.7135 10.05 2887.17

56634SMS 10.17615 31.56993 0 3106

Plan 2Voice 642.5653 316.8856 19.62 4612.55

2103SMS 39.08512 59.03361 0 932

Plan 3Voice 1011.397 505.8127 53.23 5169.68

750SMS 44.27733 60.24948 0 633

Plan 4Voice 1556.421 994.3582 168.72 11845.31

286SMS 43.13287 54.75447 0 562

Plan 5Voice 1994.418 889.3416 429.6 4334.71

93SMS 27.53763 41.02427 0 188Voice is measured in the amount of minutes consumed per monthSMS is measured in the number of messages per month

Table 2: Average usage statistics

2.2 One-side and ‘step’ nonlinear pricing

Since the firm offers a menu of three-part tariffs (second-degree price discrimination), consumer budgetconstraints are characterized not only by quantities consumed but also by the selected plan (which6

determines the amount of fixed fee to be paid). In our case, while the quantity of voice service iscontinuous, the quantity discount is discrete because users realize the benefit of nonlinear pricing only bychoosing a higher plan. Here we will call it ‘step’ nonlinear pricing. By contrast, SMS service is sold ona flat, metered basis (linear pricing). Thus the pricing is ‘one-side’ nonlinear pricing. This ‘one-side’ and‘step’ nonlinear pricing affects consumer utility maximization by generating unique budget constraints asshown in Figure 1. X-axis is the expenditure on SMS and y-axis is the expenditure on voice. The budgetline is kinked. Consider a user with the budget constraint of 2000 units (enough to select plan 5). Theuser can choose plan 5, which will give her 2117 free minutes. Then the user can not consume any SMSas it will exceed the given budget. If the user wants to consume SMS, the user needs to move to a lowerplan and save some money for SMS consumption, hence the vertical downward shift in the budget lineleading to a kink.

Under the same budget, every plan is characterized by distinctive areas indicating available amountsin voice and SMS. In Figure 1, the shaded area under the budget line shows the feasible selection area ofvoice and SMS within the chosen plan. To choose the optimal mix of voice and SMS, consumers searchfor the highest indifference curve which touches the feasible set. The graph draws the indifference curveof one consumer who chooses plan 1 and an another consumer who chooses plan 3 which maximize theirutility, respectively. In our fully articulated model described below, the total amount spent on voice plusSMS is endogenously chosen by the consumer.

This kinked budget line is consistent with the nonlinear pricing models (Moffitt 1990) and leads to aninteresting and unusual structure to the budget set, which complicates our estimation task but enablesus to identify our model as we explain later.

SMS

Unique feasible area if plan 4 is selected

Unique feasible area if plan 5 is selected

Plan 1 is the optimal plan choice for this budget curve

Plan 3 is the optimal plan choice for this budget curve

Voice

Figure 1: Feasible area conditional on a voice plan and optimal plan choice

3 Econometric model

3.1 Conceptual background

In case of many goods, a change in price of a good induces income and substitution effects that affect thedemand for the other goods. Two goods are Marshallian substitutes, if a price increase in one increases

7

demand for the other. On the other hand, the goods are complements if a price increase in one decreasesdemand for the other good.

To prove that two goods are complements, one cannot simply show that their consumptions positivelyco-vary. That is, if we find that high voice users also tend to be high SMS users, this does not implythat they are complements. Two goods are complements if an increase of price in one yields a reductionin demand for the other. As pointed out by Manchanda et al. (1999), multiple categories can be boughttogether on one shopping trip due to: (1) complementarity (or cross effect), (2) consumer heterogeneity,and (3) co-incidence. Since the main focus of this study is to examine cross effect, we need to controlthe other two confounders, heterogeneity and co-incidence. To control for heterogeneity in inherentpreferences for voice and SMS, we allow user types (as determined by the preferences for both services)to follow a probability distribution (discussed later). We also let the preferences for voice and SMS toco-vary to account for preference homogeneity. Furthermore, we use a user demographic profile to accountfor the remaining consumer heterogeneity. The varieties of co-incidence which are most likely to apply(e.g., habit persistence) can also be accommodated within the correlated user type (or equivalently viathe satiation points) as we model below.

3.2 Analytical framework

Our analytical model is based on (discrete) plan choice and (continuous) consumed quantities acrosstwo services under the given one-side and ‘step’ nonlinear pricing. Consumers are assumed to maximizeutility by making two decisions at different points on the time horizon. The consumer makes a planchoice decision among discrete alternatives at the first stage. This choice is based on the expectedoptimal consumption bundle. The consumer decides continuous quantities of service usage in the secondstage. As a result, the analytic framework takes the form of a two-stage discrete/continuous mixturechoice model.

The important early papers, that lay the blueprint for these modeling contexts, use discrete choicemodels such as logit and probit (e.g., Albert and Chib 1993) or the multinomial brand choice models(e.g., Rossi et al. 1996). But the continuous quantity decision at the second stage may not be addressedwell by the (nested) logit model as transforming continuous variables into discrete variable causes lossof information (Niraj et al. 2005). Similarly, the approach to treat different combinations – threeelement vectors of discrete plan choice and two continuous consumptions in our context – as differentmultinomial choice alternatives leads to immense numbers of alternatives making multinomial choiceunviable. Hanemann et al.(1984) develop a unified framework for formulating econometric models ofdiscrete/continuous choices in which both discrete and continuous choices aim at the same underlyingutility maximization decision. But, in their model, the alternatives for discrete choices are essentially(perfect or near perfect) substitutes and thus a consumer prefers to buy only one option (e.g., brand A overbrand B, C, and D) at any time and the continuous choice is the magnitude of the option chosen. However,in our context, the assumption that only one alternative has to be selected on a discrete choice occasionis not appropriate, because the majority of consumers select both services simultaneously. Finally andmore importantly, given that both services are selected in a mixed discrete/continuous context, separatemodeling of the two decisions – using a logit model for the discrete choice and regression models forthe continuous decision – is incorrect due to the endogeneity problem (ultimately causing inefficient

8

estimation or the omitted variable problem) if the quantity decision is not statistically independent ofthe choice decision and vice versa.4

In our context, we deal with the two goods problem, while the literature has focused on one good. Itis obvious that the two decisions (which plan to select and how many minutes in voice and how manymessages in SMS to use) are statistically dependent. This violates the basic assumption of the two-stepapproach (limited information MLE). So we have to estimate the model with full information MLE. Inthe following, we derive the joint likelihood function for the observed consumption data from generaldistributional assumptions regarding consumer heterogeneity and random error terms.

3.3 User utility specification

Since the paper contains large number of notations, for readability we first provide a table with notations.We will continue to refer to Table 3 throughout.

index i, k, t i represents a user, k represents a plan, and t represents time (month).qikt Number of voice minutes consumed by user i under plan k during month t.sikt Number of SMS sent by user i under plan k during month t.FQk Number of free quota minutes provided in plan k.Tk Fixed fee to enrol in plan k.yit Normalized outside good consumed by user i during month t.Iit Income of user i during month t.θiqt, θist User types indicating user i’s inherent preference for voice and SMS services

during month t.μq, σq Estimated mean and standard deviation of θiqt.μs, σs Estimated mean and standard deviation of θist.ρ Correlation in preference for voice and SMS.pq Marginal price of voice minute after free quota is exceeded.ps Marginal price of each SMS.εq

ikt, εsikt Error terms that captures the difference between expected and actual consump-

tion of voice and SMS.σεq, σεs Estimated variance of the error terms above.bq, bs Estimated price response parameters for voice and SMS.bint Estimated parameter indicating impact of voice consumption on SMS consump-

tion.PBCk Plan Boundary Curve: Indifference curve that separates plan k− 1 from plan k.

Users below PCBk choose plan k.FQCk Free Quota Curve: Indifference curve that separates satiated users from rest.

Users below FQCk are satiated and do not expect to use marginal minutes.While users above the curve are either at the kink or use marginal minutes.

MMCk Marginal Minutes Curve: Indifference curve that separates the users exceed-ing free quota minutes from the rest. Users above MMCk are expected to usemarginal minutes while users below the curve are either at the kink or satiated.

Table 3: Notations used in the paper

We consider individuals indexed by i =1,2,. . . ,N. The individuals choose a plan from the set ofavailable plans, indexed by k =1,2,. . . ,5 over time t =1,2,. . . ,T. They then choose continuous quantities

4To solve the problem of the two-step approach, Krishnamurthi and Raj (1988) first estimate the choice model with adiscrete choice model and then estimate the regression model based on the parameters estimated after correcting selectionbias. But, their research context is also about choice of one brand and its subsequent consumption.

9

of voice qikt and SMS sikt, conditional on the plan choice. When a user selects plan k, the user must paya fixed fee Tk to sign up for the plan, and is allowed to use a free quota of voice minutes FQk. Once theuser exceeds the free quota, she has to incur a marginal cost, pq per minute for voice. Thus, each plan isa three-part tariff that can be characterized by Tk and FQk. Users always pay the marginal price ps foreach SMS. We assume that the consumers spend the remainder of their income on an outside good yi ata normalized unit price.

We assume that the utility obtained by an individual i from selecting plan k and consuming (qikt,sikt)of voice and SMS is quadratic in quantities consumed. The utility structure is of the form:

Uikt(qikt, sikt, yit|θiqt, θist, bq, bs, bint) =1bq

(θiqtqikt − q2

ikt

2

)+

1bs

(θistsikt − s2

ikt

2

)+ bintqiktsikt + yit

bq, bs, θiqt, θist ≥ 0 (1)

The quadratic utility structure is widely modeled in the telecommunication demand literature (Econo-mides et al. 2008; Miravete et al. 2004). Note that the utility function is quasi-linear in the outside goodso that the choice of plan and consumption do not depend on income. In short, we assume that whilechange in price will induce both substitution (or complementary) and income effect, the income effect isnegligible. This assumption is reasonable and widely used since a relatively small portion of income isassigned to the telephony services (Park et al 1983, footnote 5; Economides et al. 2008).5 Low incomeeffects are highlighted in many other goods as well (see Tammo et al 2005). Though it must be stressedthat unavailability of income data is a limitation of our analysis.

In Equation (1), the first term represents utility from voice consumption, the second term representsutility from SMS consumption, and the fourth term captures utility from outside goods. As is commonlydone, we assume that the utility from outside goods and the utility from mobile services are separable.Thus consumption in mobile services does not affect the marginal utility obtained from the outside goodand vice-versa.6 However, utilities from voice and SMS services are inseparable. Thus, a change inconsumption of one service can influence consumption of the other service. This interaction is modeledthrough the third term in Equation (1) and bint captures the substitutive effect (if negative), or thecomplementary effect (if positive), or no effect (if zero). Thus our specification is very flexible. Ourutility structure assumes diminishing marginal utility of voice and SMS services and is the same for allusers.7

bq and bs represent price response parameters, respectively, which can be used to calculate the ownand the cross-price elasticity. (θiqt, θist) represents a user’s inherent preference for two services and variesacross users. Higher values of (θiqt, θist) represent higher preference for the services. (θiqt, θist) is closelyrelated to the concept of consumer satiation point – the maximum consumption level desired for a goodat any price (consumers will never demand more than the satiation point, even if the price is zero).8 The

5In our setting, most users spend less than 0.3% of their average per capita income on monthly cellular tariffs.6Some utility from outside goods (e.g., fixed phone service and broadband services) might be dependent on wireless

services. However the portion of utility from fixed phone service and broadband services is very small (or negligible) ascompared to the utility from all other human activity and there is no evidence of a consistent relationship between them.

7The second derivative of the utility function with respect to q and s is negative.8The satiation points are (

θiq+bintbqθist

1−b2intbsbq,

θis+bintbsθiq

1−b2intbsbq). The satiation point is composed of three parameters to be es-

10

notion of satiation point is widely modeled in the telecommunication demand literature (Economides etal. 2008; Miravete et al. 2004; Kling and Ploeg 1990). Notice that we allow the satiation points to varyover time, which is consistent with variation in consumption across time for a user.

Consumers first choose a plan and then choose quantities for voice and SMS. We solve the problem withbackward induction, starting with the second stage where an individual user selects optimal quantitiesfor voice and SMS, conditional on the plan choice k in the first stage, subject to the budget constraintIit :

Iit ≥ Tk + pq(qikt − FQk)+ + pssikt + yit

where

(qikt − FQk)+ =

⎧⎨⎩ qikt − FQk if qikt > FQk

0 if qikt ≤ FQk

(2)

Equation (2) indicates that the marginal price of voice kicks in only if the free quota of minutes isexceeded. Substituting the budget constraint into utility maximization objective function yields:

Maxqikt,sikt

Uikt(qikt, sikt|k) =1bq

(θiqtqikt − q2

ikt

2

)+

1bs

(θistsikt − s2

ikt

2

)+ bintqiktsikt + Ii − Tk

−pq(qikt − FQk)+ − pssikt

The first order condition is:⎧⎪⎨⎪⎩

∂Uikt

∂qikt= θiqt−qikt

bq+ bintsikt − pq = 0 if qikt > FQk

∂Uikt

∂qikt= θiqt−qikt

bq+ bintsikt = 0 if qikt ≤ FQk

and,

∂Uikt

∂sikt=

θist − sikt

bs+ bintqikt − ps = 0

Solving these simultaneously yields following demand equations.

(qikt, sikt)bint=0 =

⎛⎝ (θiqt − bqpq , θist − bsps) if qikt > FQk

(θiqt, θist − bsps) if qikt ≤ FQk

(3)

(qikt, sikt)∗bint �=0 =

⎛⎝ (θiqt − bqpq + bqbintsikt , θist − bsps + bsbintqikt) if qikt > FQk

(θiqt + bqbintsikt, θist − bsps + bsbintqikt) if qikt ≤ FQk

(4)

timated and a consumer type. If there is no cross effect (bint = 0), (θiqt, θist) is individual i’s satiation points. Due tointeraction, the satiation point in SMS service affects a satiation point in voice service and vice versa. The mutual influenceof the cross effect on satiation points critically depends on the sign of bint.

11

Equations (3) and (4) present the demand curves for voice and SMS services, in the absence andpresence of the cross effects respectively. They show that the optimal bundle in one service shifts dueto consumption level of the other service reflecting the interaction effect of two services. Therefore,comparison of the consumption bundles of two services when there is no cross effect and when there isa cross effect, enables us to see the impact of the cross effect on usage level as well as how to intuitivelyinterpret bint embedded in the interaction term.

Middle point in Figure 2 is the optimal consumption when there is no interaction between voice andSMS (bint = 0). The consumption bundle can move to one of the four directions on two dimensions ofqikt and sikt when bint �= 0 (see Figure 2) – i.e., the comparison of Equation (3) and Equation (4) presentsfour possible scenarios regarding the change of optimal consumption bundle of voice and SMS.

If the interaction effect exists, we can intuitively divide it into two groups – the symmetric scenario (1and 3) vs. the asymmetric scenario (2 and 4). Given the definition and the utility specification, the crosseffect must be symmetric, whatever its direction is: increasing in scenario (1) or decreasing in scenario(3).9 Because bq, bs, qikt, andsikt are positive, the direction of the change depends on the sign of bint

(positive or negative). In scenario 1 (bint > 0), consumption in one service induces more consumption inother service. As a result, positive bint provides evidence that one service plays a role of complementingthe other service. In scenario 3 (bint < 0), voice service is a substitute for SMS service and vice versa.Consequently, the role of bint is clear: presence or absence of bint as well as its sign captures potentialinteraction effect of these two services.

qik

Scenario 1

Scenario 3 Scenario 4

Scenario 2

sik(qikt, sikt)* when bint = 0

(qikt, sikt)* when bint 0

Figure 2: The satiation points and the cross effect

3.4 Demand function

Due to the nonlinearities of three-part tariffs, the demand functions need close inspection. In particular,there are three distinct possibilities – (i) a user’s satiation point is less than the free quota, (ii) thesatiation point is more than the free quota but the marginal price is high enough that the user does not

9Given our utility function, this symmetry can be shown by Young’s theorem: ∂U∂qikt∂sikt

is constant.

12

want to exceed the free quota minutes, and (iii) the satiation point is high enough that the user consumesmarginal minutes.

Thus within each plan, a user can be in three different regions (R1k, R2

k, R3k) depending on their type

(θiqt, θist). These regions are characterized by indifference curves, PBC k, FQC k, and MMC k which arederived in detail in the next section. These indifference curves are the threshold values of (θiqt, θist)which separate users in different regions. Figure 3 explains these regions more intuitively. We draw thesefor plan 1 and 2. The rest are analogous. PBCk (Plan Boundary Curve) curve separates plan k fromplan k + 1. Notice that PBC 1 separates plan 1 from plan 2. So there are four PBC curves. PBC 0

is simply (θiqt = 0, θist = 0). FQC (Free Quota Curve) and MMC (Marginal Minute Curve) are theindifference curves that separate the regions within a plan. FQC separates the users who are satiatedfrom the users who are at the kink. Thus the users between PBC 0 and FQC 1 (R1

1) are satiated. Similarly,MMC separates the users who are at the kink from the users who are willing to use marginal minutesby exceeding the free quota. Thus users between FQC 1 and MMC 1 (R2

1) are at the kink and the usersbetween MMC 1 and PBC 1 (R3

1) are using marginal minutes.

︸ ︷︷ ︸plan 1

︸ ︷︷ ︸plan 2

PBC 0 FQC 1 MMC 1 PBC 1 FQC 2 MMC 2 PBC 2

R11 R2

1 R31 R1

2 R22 R3

2

Figure 3: Different regions across and within plans

More formally, the demand curve within each region can be derived from Equation (3) and (4).

if PBCk−1 ≤ (θiqt, θist) < FQCk⎧⎪⎨⎪⎩

qikt = θiqt+bintbqθist−bintbqbsps

1−b2intbsbq

sikt = θist+bintbsθiqt−bsps

1−b2intbsbq

−−−−−−−−−−−−−−− R1k

if FQCk ≤ (θiqt, θist) < MMCk⎧⎨⎩ qikt = FQk

sikt = θist + bintbsFQk − bsps

−−−−−−−−−−−−−−R2k

if MMCk ≤ (θiqt, θist) < PBCk⎧⎪⎨⎪⎩

qikt = θiqt+bintbqθist−bintbqbsps−bqpq

1−b2intbsbq

sikt = θist+bintbsθiqt−bintbqbspq−bsps

1−b2intbsbq

−−−−−−−−−−−−− R3k

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(5)

where

PBCk = {(θiqt, θist|k)|U∗(R3k|k) = U∗(R1

k|k + 1)}FQCk = {(θiqt, θist|k)|U∗(R1

k|k) = U∗(R2k|k)}

MMCk = {(θiqt, θist|k)|U∗(R2k|k) = U∗(R3

k|k)}

As noted above, the demand in R1k : (PBCk−1, FQCk) is for the users who are satiated, R2

k :

13

(FQCk, MMUk) is when users are at the kink and R3k : (MMUk, PBCk) is when users are using marginal

minutes.

3.5 User heterogeneity and indifference curves

These indifference curves are derived by comparing the utilities after plugging the optimal (q∗ikt, s∗ikt) from

Equation (5) into the utility function in Equation (1). It should be noted that the optimal consumptionsin these two services are determined simultaneously.

We show that all users whose (θiqt, θist) belongs to Rk: (PBC k−1, PBC k) select plan k. As thefirst step in deriving PBC k, we classify users into 5 groups, which is equivalent to the number of plansavailable. The next axioms outline user heterogeneity based on their plan choice:

Axiom 1. If a user is indifferent between two plans (plan k and plan k + 1), the cost of plan k (“thefixed fee of plan k” + “the variable cost depending on additional usage beyond the free minutes of plank”) and the cost of plan k+1 (only the fixed fee of plan k+1) have to be identical, at the expected optimalconsumption point in voice service.10 As a result, a consumer with higher θiqt will choose a higher valueplan in order to realize benefits of nonlinear pricing scheme. Thus, the ranking of plans is monotone inθiqt.

Axiom 2. Even if the marginal cost of SMS service (ps) is identical regardless of plan choice, the planchoice is affected by θist due to the interaction. The expected optimal consumption of SMS is monotonetransformation of θiqt, which is monotone in plan choice. Therefore, the ranking of plans is monotone inθist as well.

Axiom 3. From Axiom 1 and 2, the plan choice is ordered in θiqt and θist, despite one-side nonlinearpricing. That is, the next equation always holds: Rk = {(θiqt, θist)|Uik ≥ Uij , ∀j �= k} = {(θiqt, θist)|Uik ≥Uik+1 & Uik ≥ Uik−1|k ≥ 2, Uik ≥ Uik+1|k = 1}, where Rk indicates (PBCk−1, PBCk).

Axiom 4. The indifference curve between plan k and plan k+1 can be computed by comparing utilitiesgenerated from two plans: PBCk = {(θiqt, θist|k)|U∗(R3

k|k) = U∗(R1k|k + 1)}.

Axiom 5. The shape of indifference curves (here, the slope of indifference lines) is identical across plansunder the assumption that the utility function is homothetic.

Axiom 6. Because the indifference curves do not overlap one another, indifference lines from the formulain Axiom 4 will be the boundaries dividing five plans.

Comparing the indirect utility functions across five plans, we can compute the indifference curvesseparating the two adjoining plans (From Axiom 4). The indifference curves are given by:

PBCk : θist =(2FQkpq − 2b2

intbqbsFQkpq + bqp2q + 2bintbqbspqps − 2Tk + 2b2

intbqbsTk + 2Tk+1 − 2b2intbqbsTk+1

)2bintbqpq

− θiqt

bintbq

10the actual consumption may differ from the optimal consumption due to some random shocks of zero mean. However,user can optimize plans choice only the basis of expected optimal consumption

14

We can see that the indifference curve is affected by (Tk, FQk, pq, and ps), and (bq, bs, and bint).From Axiom 5, all indifference curves have the same slope, -1/(bqbint). The interpretation of the slope isidentical to the interpretation of bint as we described in section 3.2 : a positive value of bint indicates asubstitutive relationship and a negative value complementary relationship.

As numerical illustration, we plug real numbers from our data in this equation to derive the indifferencecurve separating plan 1 and plan 2, PBC 1:

PBC1 : θist =1000 + 3bq + 6bintbqbs − 1000b2

intbqbs

2bintbq− θiqt

bintbq

FQC k and MMC k can be derived in the similar way. Plugging the optimal (qikt, sikt) from R1k and R2

k

into the indirect utility function would yield FQC k and the optimal (qik, sik) from R2k and R3

k will yieldMMC k.

FQC k : θist =FQk + 3bintbqbs − FQkb2

intbqbs

bintbq− θiqt

bintbq

MMC k : θist =FQk + 3bq + 3bintbqbs − FQkb2

intbqbs

bintbq− θiqt

bintbq

4 Model Estimation

To operationalize the theoretical model, we derive a joint likelihood function. First, we formulate theprobability of choosing a plan k and then the probability of observing the actual consumption bundle(qikt,sikt) conditional on the plan choice.

4.1 Probability of choosing a plan k

We calculate the probability of an individual i choosing a plan k from the fact that the individualchooses the plan that maximizes her utility conditional on the expected future consumptions (not realconsumption) derived from (θiqt, θist) and (bq, bs, and bint).11 The parameters (bq, bs, and bint) are to beestimated, whereas (θiqt,θist) is not observed by econometricians. We make a distributional assumptionon unobserved user types (user heterogeneity).

We assume that the distribution of the user type, f(θiqt, θist), follows a truncated bivariate normal

distribution:

⎛⎝ θiqt

θist

⎞⎠ ∼ TBN

(μ,∑)

, μ =

⎛⎝ μq

μs

⎞⎠ ,

∑=

⎛⎝ σ2

q ρσqσs

ρσqσs σ2s

⎞⎠.

Since the satiation point can never be less than zero, a truncated distribution is appropriate. Moreover,normal distribution is very flexible and tractable. We assume that (θiqt, θist) follow a joint normaldistribution rather than independent normal distributions – i.e., we allow ρ to capture the unobservedinherent association of two service consumptions, θiqt and θist. Thus, ρ > 0 indicates that the preference

11After selecting plan k, they cannot change the plan during the month.

15

for voice service is positively correlated with that for SMS. The assumption of a joint distribution allowsus to examine the cross effect by excluding the impact of inherent association (Manchanda et al. 1999).The structural parameters to be estimated are (bq, bs, and bint), the means of the distribution (μq andμs), the variances (σq and σs), and the correlation (ρ).

Given the distributional assumption, we can write the probability of a consumer choosing plan:

Prikt = Pr(plan = k|θiqt, θist) =∫ ∫

Rk

f(θiqt, θist)dθiqtdθist, (6)

where

f(θiqt, θist) =e− Q

2

/2πσqσs

√1−ρ2

1−R 0−∞

R 0−∞ f(θiqt,θist)dθiqtdθist

, Q = 11−ρ2

[(θiqt−μq)2

σ2q

− 2ρ(θiqt−μq)(θist−μs)

σqσs+ (θist−μs)2

σ2s

]

Rk =(PBCk−1, PBCk

)

4.2 Probability of consumption conditional on plan choice

In the second stage, users select a consumption bundle of voice and SMS. However, the actual demandobserved would not be equal to the expected demand derived from Equation (5). The difference be-tween the “actual” consumption and the “expected” consumption occurs due to unobserved noise that isunanticipated by consumers. Thus, the difference reflects a random shock (or measurement error) a usermay experience in a given month. For the empirical estimation, we add an error term in the demandfunction as an additive form following Burtless and Hausman’s (1978) approach. Absent an error term,all consumers in the R2

k region would always cluster at the kink – a fact that is inconsistent with thedata. Thus the realized demand is, qikt = E(qikt) + εq

ikt, where the expected demand E(qikt), is derivedin Equation (5). The SMS demand curve is derived analogously. We assume that the distribution of errorterms, h

(εq

ikt, εsikt

), follows the independent bivariate normal distribution:

⎡⎣ εq

ikt

εsikt

⎤⎦ ∼ BV N

⎛⎜⎝⎛⎝ 0

0

⎞⎠⎛⎝ σ2

εq 00 σ2

εs

⎞⎠⎞⎟⎠.

Assuming f(θiqt, θist) and h(εqikt, ε

sikt) are stochastically independent, probability of observing the

consumption depends on plan choice k, and the region Rk within the plan. Recall from Figure 3 thata user could be satiated, at the kink, or using marginal minutes. Therefore probability of observing(qikt, sikt) conditional on plan k is

g(qikt, sikt|k) =

∫ ∫R1

k

h(εqikt, ε

sikt)dF +

∫ ∫R2

k

h(εqikt, ε

sikt)dF +

∫ ∫R3

k

h(εqikt, ε

sikt)dF

∫ ∫Rk

dF(7)

where dF = f(θiqt, θist)dθiqtdθist. Regions Rk are as defined previously.

16

4.3 Joint likelihood function

Now we can derive the joint distribution of a user i choosing a plan k and then choosing (qikt,sikt)conditional on user type. The joint likelihood function for a user i is Prikt(k|•)× gikt(qikt, sikt|•, k). Thelikelihood function across both individual i and time t is:

L =∏i

∏t

(Prikt(•) × gikt(•)

)=∏i

∏t

(∫ ∫Rk

h(εqikt, ε

sikt)f(θiqt, θist)dθiqtdθist

) (8)

Any statistical or econometric model makes an important trade-off between “an analytically tractable,but parametrically restrictive specification” and “analytically complicated, but parametrically flexiblespecification” (Seetharaman et al. 2005). In the similar vein, our formulation also imposes two nonlinearconstraints derived from the concavity condition of utility function and from the condition of monotoneordering of indifference curves:

(i) 0 < b2intbsbq < 1

(ii) bq < 343 (1 − b2

intbsbq)

We cannot obtain closed form expression for the joint likelihood function. Thus we need to computeit numerically. We estimated the model in two ways: (1) maximum likelihood estimation (MLE) withdirect numerical approximation (quadrature integration) and (2) maximum simulated likelihood estima-tion (MSLE) using Monte Carlo methods. MLE imposes a significant computational burden involvedin numerical integration restricting the sample size. MSLE on the other hand places less computationalburden and, hence, we report the estimates from MSLE. For MSLE, we selected f(θiqt, θist) as an impor-tance function. The simulated log-likelihood function is the average value of the function of h(εq

ikt, εsikt)

over the importance function. We thus maximize the simulated log-likelihood function subject to theconstraints:

ln L ≈∑i,t

ln

(Eh(εq

ikt,εsikt

)[Tr × f

(θiqt, θist

)])(9)

In Equation (9), Tr is a truncation compensation factor. To sample from a bivariate normal distribu-tion of (θrng

iqt , θrngist ), we began with draws from two standard normal distributions of (erng

1 , erng2 ) and then

used the Cholesky decomposition to transform the random variables. By matrix algebra, it is possible todecompose the bivariate normal distribution in the following way,⎛

⎝ θrngiqt

θrngist

⎞⎠ =

⎛⎝ μq

μs

⎞⎠+

⎛⎝ σq(

√1−ρ2) σqρ

0 σs

⎞⎠⎛⎝ erng

1

erng2

⎞⎠

When we maximized the simulated log-likelihood, we used the same set of random draws for everycomputation in order to achieve continuity (1000 draws). That is, each observation has its own unchangingvector of 1000 draws. We used the BHHH (outer product of gradients) estimator to compute asymptoticcovariance matrix of the simulated maximum likelihood estimator.

17

4.4 Identification Issues

As the three choice decisions, [(k), (qikt,sikt)] are the consequences of a single utility maximization for anindividual; the model ensures that these decisions provide, in combination, the greatest possible utilityto the individual. The parameters to be estimated in this study are grouped into two categories: (1)three structural parameters embedded in the utility function (bq, bs and bint) and, (2) distribution-relatedparameter groups consisting of (μq, μs, σq, σs, and ρ) for the user type distribution, and (σεq and σεs)for the measurement error distribution.

First, note that all distributional parameters are readily identified due to the systematic variationin plan choices and consumptions across individuals. The mean value of voice (μq) and SMS (μs) withassociated variance σq and σs are identified due to variation in consumption across users and time. σεq

and σεs are identified due to differences in expected and actual consumption. Analogously ρ is identified.

The key price response parameters need closer examination. bq (price response parameter to voiceservice) is readily identified as users face different marginal prices depending on whether they are satiatedor not. In particular, consider a user type θiqt who is indifferent between plan k and plan k + 1. In plank, the user is using marginal minutes while in plan k +1, the user is satiated. Thus, for a slight variationaround such a θiqt, the user faces different marginal costs affecting her voice consumption (a user of typeθiqt − ε is using marginal minutes while a user of type θiqt + ε is satiated, leading to different consumptionamount by potentially the same θiqt type). By analogy, bq is also identified off the kinks within a plan(recall three different regions, (R1

k, R2k, R3

k) within a plan force a user to face different price schedule).In contrast, bs is not directly identified because there is no change in SMS pricing – the marginal costof SMS service is constant even around the kinked budget constraint. However, variation in the priceof voice minutes should impact SMS consumption through the hypothesized cross effect and thus bs

is (indirectly) identifiable. Our key parameter of interest bint is identified through changes in marginalprices for voice as explained above. Moreover, whenever a user exceeds her free quota limits, her marginalprice of voice changes from 0 to 3. This change in voice price provides an opportunity to identify howSMS consumption changes. Since identification of bint is key to our paper, we explain in more intuitivedetail how bint is potentially identified in section 5.2. It is noticeable that the key parameters (bq,bs andbint) are simultaneously estimated not just through likelihood maximization but also the unique pricingscheme causing the kinked budget constraint.

5 Result and Discussion

The estimation results by maximizing Equation (9) are given in Table 4. We estimate the model witha full sample, and then split it along some demographic variables. The first three rows are the keystructural parameters and the rest are the estimates for distributional parameters.

We first focus on the distributional parameters (row 4 and below). Most of these estimates areconsistent with our data. For example, μq and μs capture the mean voice and SMS consumptions whichmatch well with the means reported in summary statistics in Table 2. These parameters are estimatedprecisely. σεq and σεs capture measurement error and these estimates are fairly high suggesting that the

18

Wholesample

Users withAge<30 30≤Age<40 Age≥40 Female Male

bint -0.35∗∗

(0.07)-0.53∗∗

(0.11)-0.48∗∗

(0.05)-0.38∗∗

(0.07)-0.59∗∗

(0.19)-0.33∗∗

(0.03)bq 7.22∗∗

(1.11)5.27∗∗

(0.80)8.53∗∗

(0.68)9.24∗∗

(1.12)7.31∗∗

(2.32)8.51∗∗

(0.55)bs 0.12∗∗

(0.02)0.06∗∗

(0.01)0.08∗∗

(0.01)0.12∗∗

(0.02)0.04∗∗

(0.01)0.10∗∗

(0.01)μq 283.11∗∗

(1.26)334.07∗∗

(2.35)272.81∗∗

(1.14)208.61∗∗

(2.76)290.01∗∗

(1.54)279.80∗∗

(1.40)μs 11.58∗∗

(0.27)17.41∗∗

(0.31)10.49∗∗

(0.73)9.97∗∗

(0.47)15.24∗∗

(0.25)10.57∗∗

(0.21)σq 134.82∗∗

(1.03)161.72∗∗

(5.29)147.39∗∗

(5.17)148.60∗∗

(2.95)136.75∗∗

(2.06)132.75∗∗

(1.19)σs 23.03∗∗

(0.11)26.52∗∗

(0.09)17.37∗∗

(0.18)18.08∗∗

(0.29)22.44∗∗

(0.05)18.97∗∗

(0.05)σεq 200.45∗∗

(0.14)214.95∗∗

(0.15)165.30∗∗

(0.24)155.01∗∗

(0.44)174.13∗∗

(0.06)192.75∗∗

(0.12)σεs 17.83∗∗

(0.003)21.97∗∗

(0.01)11.58∗∗

(0.003)14.24∗∗

(0.01)17.12∗∗

(0.004)15.27∗∗

(0.003)ρ 0.83∗∗

(0.01)0.84∗∗

(0.02)0.89∗∗

(0.01)0.63∗∗

(0.02)0.85∗∗

(0.01)0.71∗∗

(0.01)N 59,866 22483 29,520 7,863 32,592 27,274Log-likelihood

-606,520 -235,480 -299,250 -79,558 -332,790 -276,630

Standard errors are shown in parentheses.∗Significant at p < 0.05 ∗∗Significant at p < 0.01

Table 4: Estimated Parameters

difference between actual and expected consumption is high – that is, users choose suboptimal plans (atleast ex-post). This is consistent with the prior literature (Miravette, 2000). The intrinsic associationbetween satiation points in the two services is significantly positively related (ρ = 0.83). That is, aheavy user of one service is likely to be the heavy user of the other service regardless of substitutionor complementary effect. This suggests that controlling for the intrinsic association of two services isimportant for an unbiased estimate on the cross effects of two services.

The first three rows are the price response structural parameters. One of our key interests is thecross-effect estimate on bint. The sign of bint is negative and it is statistically significant. The estimateis consistently negative across all demographic segments. This provides an evidence that voice and SMSform a substitutive relationship in our data. The negative and significant estimate indicates that: (1)the real consumption levels, which we can observe, are lower than the satiation points, which we cannotsee, in both services, (2) the optimal consumption of voice (or SMS) decreases as the consumption of theother service goes up because the consumption in one service partially satisfies the satiation points inthe other service. The estimates on bq and bs are also sensible and significant. Since the estimated bq

is significantly greater than bs, it seems to suggest that the voice consumption is more sensitive to pricechange.

We next split the data based on demographic factors (age and gender) and analyze the difference in the

19

key parameter estimates across sub-groups. The results are shown from column 3 to column 7. Both priceresponse parameters are significant in all groups though their magnitudes varies across groups. Youngerusers, on average, have higher estimated mean consumption in both services (μq, μs) consistent with theraw distribution of data. However, we also find a stronger substitution effect (bigger bint in an absolutevalue) in the younger group than in the older group. Interestingly, there is less intrinsic correlation (ρ)between voice and SMS for older users than younger ones. Females are more likely to consume more SMSthan males and have a higher estimated substitution effect. Also, notice that estimated ρ for males ismuch smaller than females.

The estimated values of bq, bs, and bint do not provide a clear picture of differences across groups.We now discuss the implication of bint as well as the two price response parameters by calculating own-and cross-price elasticities.

5.1 Own- and cross-price elasticities

To understand the true economic significance of estimated parameters, we calculate own- and cross-priceelasticities using the estimates of bq, bs, and bint. Since we need marginal prices for both voice andSMS to estimate elasticities, and a user experiences the marginal price of voice only if the user is inregion R3

k, we use the demand Equation (5) in region R3k for estimating elasticities. Straightforward

manipulation of the equation leads to the own-price elasticity of voice as Eq = −3bq

/q(1 − b2

intbsbq)

and the own-price elasticity of SMS as Es = −3bs

/s(1 − b2

intbsbq). The cross-price elasticity of voicewith SMS (% changes in voice consumption in response to % change in SMS price) can be calculated byEq,s = −3bintbqbs

/q(1 − b2

intbsbq) and the cross-price elasticity of SMS with voice can be calculated by

Es,q = −3bintbqbs

/s(1 − b2

intbsbq).

Recall that our demand curves are linear and, therefore, the elasticities depend on quantities. Putanother way, the reaction to proportional price changes will be different depending on the quantitiesconsumed. This is the reason we can not directly infer the magnitude of substitution by just lookingat the estimate for bint. Also, note that the cross price elasticities differ due to scaling. People usesignificantly large number of voice minutes as opposed to number of SMS. Since we observe the changein the marginal price of voice in our data (SMS prices remain unchanged) we will predominantly focuson the elasticity of SMS with voice (Es,q). Below in Table 5, we report the elasticities at the mean valuesfor voice and SMS consumption. Given the signs of the estimated parameters, the own-price elasticitiesare negative and the cross price elasticities are positive.

We start with the cross-price elasticities. The elasticity of SMS with voice is estimated to be smallwith a magnitude of about about 0.08. Roughly this suggests that if the price of marginal voice minutesincreases by 100%, the SMS consumption will increase by about 8%. Put another way, if the price ofmarginal minutes were to increase from 3 to 6, the number of SMS will increase by one message to about14 messages (mean number of SMS is about 13, an 8% increase translates to about one message). Lowvalues of cross-price elasticities suggest that while SMS acts as a substitute for voice, the magnitudeof this substitution is low. It seems that the users in our sample view voice and SMS as differentiatedservices which serve to different applications and needs. Therefore, a choice to send a SMS does notsignificantly diminish the need to make a voice call and vice-versa.

20

Mean-usage price elasticities

Whole SampleMean Own-price elasticity Cross-price elasticity

Voice 285 Eq = -0.085 Es,q = 0.078SMS 13 Es = -0.030 Eq,s = 0.003

Users with Age < 30Voice 330 -0.052 0.032SMS 17 -0.011 0.001

30 ≤ Age < 40Voice 265 -0.114 0.116SMS 10 -0.028 0.004

Age ≥ 40Voice 204 -0.161 0.188SMS 8 -0.053 0.007

FemaleVoice 287 -0.085 0.041SMS 14 -0.009 0.002

MaleVoice 274 -0.102 0.092SMS 10 -0.033 0.003

Plan 1Voice 249 -0.097 0.100SMS 10 -0.039 0.004

Plan 2Voice 643 -0.037 0.026SMS 39 -0.010 0.001

Plan 3Voice 1011 -0.023 0.022SMS 44 -0.009 0.001

Plan 4Voice 1556 -0.015 0.023SMS 43 -0.009 0.0006

Plan 5Voice 1994 -0.012 0.036SMS 28 -0.014 0.0005

Table 5: Estimated own- and cross-price elasticities

21

The estimated own-price elasticities are small. The low values of own-price elasticities of voice andSMS suggest that users do not respond to price changes very aggressively (at least at the mean values).The numbers suggest that a 100% increase in the price of voice minutes would lead to about 8.5%reduction in demand. Thus if price of voice minutes were to increase to 4 from 3 (a 33% increase), onaverage it would lead to a reduction of about 8 minutes. Low own-price elasticities are consistent withthe previous research on land-line telephony usage. The price elasticities of fixed line demand in previousstudies range from -0.1 to -0.5. Garbacz and Thompson (2003) report that the demand for local serviceis highly inelastic (-0.006 to -0.011). Park et al. (1983) use random experimental data and report thatelasticity is about -0.1 in absolute value. Kling and Ploeg (1990) show that the price elasticity of fixedphone service is in the range of -0.1. Andersson (2006) report low own price elasticity for mobile telephony(about -0.2). Generally, users exhibit low elasticity to more necessary services. The low number could bea reflection of the fact that mobile services are increasingly becoming necessary to users. In fact, in manycountries, mobiles phones are becoming the only communication device users retain. Thus low elasticitiescould be the manifestation of these changing structures.

SMS service is far less elastic than voice service. This could be due to the relatively small consumptionlevel – the price elasticity is calculated with not only price response parameters but also average usage(the average of SMS consumption is around 11 messages). That is, consumers are likely to be satiatedwith a relatively small number of messages and might respond to the marginal price of SMS service farless than that of voice service.

At first blush, the low elasticity levels seem inconsistent with a familiar result from the neoclassicaltheory of the firm that a firm does not set prices in a region of its demand where the elasticity is less thanone. However, there are a number of reasons why this is not so. First, the elasticity we are measuringis not the elasticity relevant to the standard result. Consumers might respond to an increase in ourfirm’s prices both by reducing minutes consumed and by substituting to the products of other firms. Thestandard result applies to the sum of these two effects, and we examine only the former of the two. It iseasy to imagine the latter effect being the larger of the two. Another way of saying this is that we arenot measuring the residual elasticity facing the firm (what the standard theory is about) but the marketelasticity of the consumers who happen to have chosen this firm. Second, the standard result applies onlyto static models: in a setting with stickiness in demand or other interesting dynamics, the result neednot apply, and firms may price at an inelastic point.

The results show that the price elasticities are different across age-based and gender-based segmentedgroups. The findings of a big variation in price elasticities across individual demographic profiles couldbe informative for practical managerial implication. First, we find that the younger users are, on average,more inelastic than the older group for both the own and the cross-price elasticity. We do not haveinformation regarding individual income. But, it is generally believed that the older users have a higherincome and they are expected to be more inelastic to price change. Therefore, this is somewhat counter-intuitive and provides some insight in understanding mobile service. It could be that the parents arepaying the bills for youngsters and that reduces their elasticity, or that the young users perceive mobileservices as more necessary than the older users. Since the older users are more elastic, we conclude thatwhen the marginal cost of SMS increases, the older users are more likely to change the communicationtool from SMS to voice than the younger users.

22

The Female users are more inelastic than the male users in both services. And the cross-price elasticityof voice in the female group is half that of the male group. Thus, it suggests that men are more likely toconsider SMS as a substitute to voice than women.

Given our linear demand curve, the variation of own- and cross-price elasticities across plans is rea-sonable. As users select a higher plan, they show less sensitive price response behavior. This is to beexpected as the average consumption is increasing in plans.

5.2 Alternative evidence of substitution effect

One key goal of this paper is to identify the interaction of voice and SMS. We explained the details ofour identification strategy behind bint earlier. However, in a structural framework, there may be worriesthat nonlinearities in the likelihood function are driving identification. To provide more robustness toour analysis, we now provide a more intuitive evidence of how SMS is a substitute for voice.

First, note that when users’ voice consumption is below the free quota in their selected plans, usersface zero marginal cost for voice but positive marginal cost for SMS. Once they exceed the free minutes,the voice minutes also incur a marginal cost. Thus, if SMS is a substitute (or complement), we shouldexpect a significant jump (drop) in the SMS consumption when the free quota is exceeded. The free quotafor plan 1 is 350 minutes. Thus a user exceeding 350 minutes in plan 1 would pay for voice minutes.However, a user who signs up in plan 2 would not worry about the 350 minute limit as the free quotalimit for plan 2 is 517 minutes. Therefore, we compare the user group in plan 1 with the user group inplan 2 and see how the SMS consumption changes when users exceed 350 minutes in both plans. Moreprecisely we run the following regression, where i indexes users and t indexes time:

SMSit = β0 + β1qit + β2DFQk+ β3(qit − FQk)+ + εit (10)

where,

DFQk= 1 if qit ≥ FQk, otherwise 0.

(qit − FQk)+ = qit − FQk if qit ≥ FQk, otherwise 0.

DFQkcaptures the jump (drop) in SMS consumption before and after the free quota (or incurring

a marginal cost per minute). Thus a positive and significant estimate on this dummy for plan 1 usersshould provide the evidence of substitution effect. We report the results of this regression in Table 6.We run the regression for users selecting plan 1 and for users selecting plan 2. We confirm from Table6 that there is an abrupt increase of SMS consumption at the kinked point (of 350 minutes) in only theuser group selecting plan 1 (notice the significant coefficient (p = 5%) of dummy DFQk

only for the plan1 users but not for plan 2).

Figure 4 captures this jump in SMS consumption around the free quota boundary. SMS consumptionincreases with voice (positive correlation) but the jump in SMS consumption around free quota providesa strong evidence of a substitutive relationship between voice and SMS.

We find the same results when considering the individual fixed effect. We tested the same model

23

User Group selecting Plan 1 User Group selecting Plan 2Voice 0.01∗∗

(0.001)0.12**(0.06)

DFQk1.03∗∗

(0.54)2.55(7.2)

(Voice-350)+ 0.013∗∗

(0.002)-0.12(0.06)

Constant 6.97∗∗

(0.38)-4.26∗∗

(15.66)N 56634 2103Standard errors are shown in parentheses∗∗ Significant at p < 0.05

Table 6: Substitution effect of SMS for voice service

�

�

���������

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

��

��

��

voice

sms

FQ

Figure 4: Evidence of substitutive relationship of voice and SMS

in the narrower range of voice consumption: qi = [150, 550]. The dummy is still significant, providingrobust support for substitution effect. In summary, we believe that the substitution effect identified inour structural model is robust and consistent with our data.

5.3 Policy Experiments

A key advantage of a structural model is that one can perform policy experiments and a “what-if”analysis. That is, we can analyze what happens to a firm’s demand and hence revenue (or profit) “if thefixed fee increases by 1%” or “if the firm decreases the free quota by 1%.” One of the goals of this paperis also to provide some actionable recommendations to managers. Thus conducting policy experimentsprovides useful information regarding the impact of change on the firm’s revenues as well as profitability.

It should be noted that the nonlinear pricing and the kinked budget line make the interpretationof estimates difficult. In particular, a change in any of the key strategic (decision) variables cannot be

24

analyzed in isolation because the change likely causes multiple changes in consumers’ plan choice andconsumption behavior. As a result, estimating price elasticity alone is not sufficient enough to highlightthe impact of prices on consumer demand. For example, the change in the marginal cost of voice minuteswill not only affect the demand for users consuming marginal minutes (region R3

k) but will also forcemore users on kink point R2

k. Therefore, the change will potentially affect the plan choice probability aswell – i.e., a unit price increase in voice for a plan can impact the profitability of every plan. Thus thechange in marginal price of voice or SMS within or across plans is likely to have indirect effect on thedemand for all other plans and the associated consumption level.

Moreover, another key strategic variable available to the firm is the fixed fee of every plan. Similarly,the firm can increase or decrease the number of free minutes available in each plan. Since the fixed fee (orfree minutes conditional on each plan) does not vary in our data, the impact of changes in fixed fee cannot be readily estimated. But, our policy experiment based on a structural model outlined in our paperallows us to estimate the impact of a change in all the strategic variables more completely by simulatingvarious counterfactual possibilities. Again, this analysis provides substantial advantages over a reducedform model.

We perform various simulations. In particular, we examine how changes in the strategic variables affectthe firm’s revenue. Note that we outline only the impact on firm revenues. However, any other metricssuch as probability of plan choice, or changes in demand can also be readily calculated. The strategicvariables we manipulate are : (1) change in the marginal price of voice and SMS, both separately andsimultaneously, (2) change in the fixed fee, and (3) change in the free quota minutes.

To carry out this exercise, we randomly generate around 5000 of (θiqt, θist) based on the estimateddistribution-related parameters for policy experiments. Table 7 shows the plan choice distributions ofboth the generated data and the collected data, indicating that the model fits the data reasonably well.That is, the structural parameters are consistent with our large sample, and thus the data generated forthe experiments are well representative of the “real world” data we collected.

Plan 1 Plan 2 Plan 3 Plan 4 Plan 5Data randomly generated 0.96% 0.04% 0.00% 0.00% 0.00%Data collected 0.95% 0.04 % 0.01% 0.00% 0.00%

Table 7: Plan choice distribution

The first exercise is simply aimed at evaluating the effect of change in strategic variables withoutconsideration of consumer differentiation across demographic segments. We calculated, for each gener-ated (θiqt, θist), the optimal plan choice and subsequently the optimal consumptions of both services.Given that, we can compute the firm’s revenue from the expected consumption behaviors. We can thenrecalculate the revenues by changing any strategic variable. The upper part of Table 8 shows the changeof revenue derived from “one unit change” of every strategic variable. But, a unit increase in the marginalprice of voice is not directly comparable to a unit increase in the fixed fee due to scaling. Another possi-bility is to consider “%” change in the prices. However, a 10% change in the marginal price of the voice isnot the same as a 10% change in the fixed fee. To keep the comparisons reasonable, we let the marginalprices of voice and SMS to change by 10% and the prices of fixed fee and volume of free quota to change

25

by 5%.12

Users can respond to the change of the pricing scheme either by reducing the consumption level orby leaving the firm (i.e., switching mobile operators or giving up mobile communication). In order toincorporate the hypothetical defection behavior, we assume that consumers leave the firm when theirsurplus (utility level) from the mobile service goes below a certain threshold. To set this threshold,we rank order consumer surplus. The threshold is set at the lowest surplus level. As we change theparameters, if a consumer’s surplus falls below the threshold, we consider the consumer leave the firm.We applied this condition to all policy experiments we performed.13 However, it must be noted that wecannot systematically and fully specify consumers’ defection behavior in our policy experiments becauseof lack of detailed data.14

One unit change of strategic variablesOne unit MPincrease inboth Services

One unit MPincrease invoice

One unit MPincrease inSMS

One unitFixed Feeincrease

One minuteFree MinuteDecrease

RevenuesIncrease

2.94% 0.87% 2.06% 0.12% 0.15%

Normalized unit change of strategic variables10% MPincrease invoice

10% MP in-crease in SMS

5% Fixed Feeincrease

5% FreeMinute De-crease

RevenueIncrease

0.26% 0.62% 3.8% 3.1%

Table 8: Simulation of change of unit pricing scheme

Compared to change in the marginal price of both services, change in the fixed fee (or free quota)has far greater impact on the firm’s revenue. This is consistent with our general expectation. A changein the fixed fee or the free quota affects all consumers by increasing their fixed cost. However, change inthe marginal cost of voice has little effect on the users not exceeding the given free quota – according tothe data, only one third of the observations (20,346) incur marginal costs across all plan. Further, theresults suggest that a decrease of free minutes can increase revenue, but the most effective strategy is toincrease the fixed fee somewhat. A change in the marginal price of SMS service has a bigger influenceon the revenue than a change in the marginal price of voice. At a glance, this is inconsistent with theinference from the calculated price elasticities of demand. But the results are attributed to the differenceof average consumption levels, which we highlighted earlier.

12One could potentially calculate the equivalent fixed fee increase or free quota decrease for a unit price increase inmarginal voice minute. Based on the usage, individual users consume 39.75 additional voice minutes beyond the given freequota. A user pay an average price of 1.023 units for a voice minute. Therefore, one unit marginal price increase in theprice of a voice minute is equivalent to increasing the fixed fee by 38.85 units or decreasing the free minutes quotes byabout 39.75 minutes. Similarly, the average consumption of SMS is 11.8, one unit increase of per minute marginal price forvoice is comparable to about 0.296 unit increase of per message marginal price. We performed our simulations with thisalternative specification as well and results are comparable. They are available upon request from authors.

13This approach is based on the assumption of cardinal utility and enables us to incorporate the negative repercussionsof the change of strategic variables in the policy experiments. For example, the price change such as the increase of fixedfee would make the mobile services more unattractive, at least for the users with low (θiqt, θist).

14We essentially outline only small price changes and one would expect that for the small price changes, consumers’defection probability is small. Thus, for small price changes, we treat the firm as a monopolist. So the policy experimentssuggest how the change of pricing scheme will affect the direction of revenues.

26

We further perform policy experiments across different demographic groups. We generated (θiqt, θist)separately in every group based on the estimated parameters of the corresponding groups. Table 9 showsdistinct difference in the effect of the changes of strategic variables across demographic segments as wellas across selected plans.

10% MPincrease invoice

10% MP in-crease in SMS

5% Fixed Feeincrease

5% FreeMinute De-crease

Age<30

Revenue Increase 0.61% 0.94% 3.3% 4%

30≤Age <40

Revenue Increase 0.17% 0.44% 3.80% 2.91%

Age≥40

Revenue Increase 0.10% 0.55% 3.50% 1.84%

Female

Revenue Increase 0.08% 1.07% 3.80% 1.54%

Male

Revenue Increase 0.70% 0.60% 3.80% 2.92%

Plan 1

Revenue Increase 3.65% 2.92%

Plan 2

Revenue Increase 0.14% 0.16%

When conducting policy experiments in every segment, we generate (θiqt, θist) based onthe estimated parameters of the corresponding groups.

Table 9: Policy experiment across Demographic groups and plans

The effect of change in the marginal prices is far higher in younger users (Age < 30) than in olderusers (Age > 30), consistent with their calculated price elasticities. In particular, it is noticeable thatthe effect of an increase in the marginal price of voice is greater in younger users than in the others byaround 6 times. We conjecture from this findings that younger users are more likely to incur marginalcost than older users.

A change in the marginal prices or the free minutes is more effective in younger users than in olderusers while an increase in the fixed fee is the best strategy for older users. The simulation shows thatthe effect of change in the free minute is greatest in the younger user group. However, interestingly, theeffect of the fixed fee increase is smallest in younger users. As a result, the firm can increase its revenuewith by changing the fixed fee for older user group than changing any other strategic variable. Youngerusers are likely to use as much free minutes available and thus the decrease of free minutes turns out tobe the most effective tool to increase revenue for that group.

Comparing the price-elasticities between male and female groups, we found female users are moreinelastic than male users in both services. However, the simulation shows that change in the marginal

27

price for voice is more effective for males while change in the marginal price of SMS is more effectivefor females. Thus, this result suggests that our policy experiments provide more useful information byaccommodating the multiple changes caused by changing one variable.

Another exercise is to compare the impact of the changes in the fixed fee or the free quota acrossavailable plans. We increase (decrease) the fixed fee (free quota) of a selected plan by leaving the otherplans unchanged. The simulation shows that an increase in the fixed fee is the most effective strategy toincrease revenues as shown in the lower part of Table 8. Majority of users select plan 1 or plan 2 andthus effects of change in the fixed fee (or the free minutes) in other plans are ignored.

5.4 Discussion and implications of our findings

Our results offer two clear implications and contributions. The first contribution is academic. We offer amethod to estimate own- and cross-price elasticities in the context of nonlinear tariffs involving two goods.Nonlinear tariffs are offered in many settings and most popularly in the wireless telephony. Firms are alsoincreasingly offering multiple services. Due to complexity of tariffs, the customer usage data availableto firms and researchers is also complex. This precludes use of simple demand estimates. Despite thecomplexity of data, firms still need to tease out how multiple services interact and how elastic consumersare to prices. We believe that our paper extends the literature and provides a framework to analyze suchdata in a rigorous but tractable fashion. As the wireless market evolves and other 3G (third generation)data services become routine (e.g., web browsing), our model can be extended to incorporate additionalservices and their interactive effect on voice and SMS.

In a similar fashion, our results have implications for firms offering a bundle of multiple services.Firms are increasingly offering bundled services and applications to users, especially in cellular markets.Bundling is used for price discrimination, increasing customer loyalty, as well as introducing new services.However, bundling multiple services also requires careful understanding of how those services interact.When introducing a new service, firms tend to give them away at no cost by bundling them with ex-isting services. New services thus can be diffused effectively. However, such bundling requires carefulconsiderations of whether the services are significant substitutes. If the services are complements oreven independent, then such strategies can be highly effective (Andersson 2006). Otherwise, significantpopularity of substitutive services offered at a lower price can have large cannibalization impact on keyrevenue earning services of a firm.

Table 10 shows the results of the policy experiments regarding bundling strategy of voice and SMS. Asthe estimated substitutive relationship between two services indicates, the provision of “free” SMS cannotincrease the consumption of voice whereas the free SMS decreases the consumption of voice. Therefore,the bundling of voice and free SMS reduces the firm’s revenues.

Bundling of voice and free SMS

The number of free SMS 1 2 3 4 5 10

Revenue Change -0.36% -0.71% -1.04% -1.36% -1.66% -2.99%

Table 10: Policy experiment regarding bundling of voice and SMS

28

Moving forward, these issues are going to be critical for firms as cellular platforms increasingly offermultiple services and applications, sometime provided by third parties. Availability of multiple servicesand applications tend to increase the value of a cellular platform. However, they can also compete directlywith the firm’s own services. Understanding how a new application or a service would interact with thefirm’s portfolio will be critical for a platform’s profitability. This is one of the reasons a firm like Apple,for a long time, explicitly prohibited users from downloading VoIP applications (like Skype) on theiriPhones which directly cannibalizes its voice services. Currently, iPhone and “Google Voice” are engagedin a similar battle. We believe that our model provides a useful framework to analyze these situationswhich are going to be increasingly commonplace.

Finally and more importantly, our results have useful managerial implications. As we pointed out,complexity of nonlinear tariffs also make it difficult to interpret how changes in key strategic variablessuch as marginal cost or fixed fee would impact firm demand and hence profitability. As outlined in Table8, 9, and 10, our policy experiments provide a useful decision support to the firm. Specifically, our resultscan be used to design optimal tariffs by utilizing the results of the policy experiment. Given the userheterogeneity in our data set – most of the users have selected plan 1 –, the firm could have potentiallyexploited user heterogeneity better by offering more plans at the lower level. Considering everything, ourresults suggest that the firm’s current tariff structure is potentially sub-optimal.

6 Conclusion, limitation and further research direction

Our paper seeks to examine the interaction of voice and SMS services provided by a wireless operators.The tariff structure offered by the operator is nonlinear and the customer decision making is sequential(choice of a plan first and the consumption amounts of voice and SMS later). Moreover, customersconsumes both voice and SMS conditional on a plan choice. We start by specifying a utility structureand derive consumer demand for these services. Our framework accounts for endogeneity of plan choiceand subsequent consumptions. Thus, our model provides an estimable structure which takes into accountthe unique nature of wireless demand. We estimate the model with a unique and rich individual-levelconsumption dataset, which has detailed information on each consumer’s plan choice and then subsequentconsumption quantities for voice and SMS. Using the data, we estimate, among other parameters, thecross-price effects of voice and SMS. Our model accounts for customer heterogeneity in terms of theirinherent preference for voice and SMS.

Our results show that voice and SMS services are Marshallian substitutes. However the magnitudeof substitution is small. We find that, on average, the cross-price elasticity of voice and SMS is low andabout -0.08. That is a 10% increase in the price of voice minutes would lead to about 0.8% increase inSMS consumption. We also estimate the own-price elasticity of voice and SMS. We find that the own-price elasticity of voice is about -0.085 while the own-price elasticity of SMS (though it is not identifieddirectly) is about -0.030. The low estimated elasticity for voice is comparable to what researcher havefound in the land-line telephony studies (low price elasticities ranging from -0.1 to -0.2). We also findthat in many cases, consumers who prefer higher levels of voice consumption also have preference forSMS consumption. In short, there is a strong inherent correlation between these services(ρ = 0.83). Wehighlight how controlling for this inherent preference is important for estimating the cross effects. To test

29

the robustness of our identification, we also perform an intuitive regression analysis. The regression usesthe change in voice service’s marginal price once the user exceeds the allowable free minutes of a selectedplan. The estimates from the regression exercise confirm the substitutive relationship of voice and SMS.

We also explore how user sensitivity varies depending on demographic characteristics. We find thatolder users are more price-sensitive in both services as well as exhibit higher cross-price elasticity. Wefind that there is little difference between the consumption patterns of males and females compared toage-based segmented groups. The extent of substitution effect and price elasticity somewhat depends onusers’ demographic factors. We then conduct some counterfactual policy experiments to examine howchanges in key strategic variables affect firm profitability. We outline how our model allows us to estimatethese effects. The last point is particularly important because the contribution of this paper goes beyondthe rich dataset we have collected. It is also the structural model we build that allows us to identify andestimate key elasticity parameters that otherwise would not be possible with a naıve reduced form model.Thus our methodology provides us with insights into consumer behavior that otherwise would escape us.Thus, our research provides interesting avenues for future research in an important and growing field ofcellular voice and data communication.

While the richness of the data is a key strength, it is not without limitations. We do not have detailedinformation on consumer (disposable) income. Therefore, our analytical framework doesn’t reflect on howindividual users allocate their monthly budget to mobile communication and outside goods. In reality,users are expected to make decisions of budget allocation by comparing the utility from mobile serviceand that from others. We cannot accommodate this feature in our model. Our data is also limited toone firm. In particular, the own-price and the cross-price elasticities should be interpreted with cautiondue to lack of competitor data. Similarly, our results should be interpreted as conditional on firm choice.Therefore, our measure is focused on only the consumer consumption reduction behavior to price increase– this limited research view is partly applied to the counterfactual policy experiments we conducted. Ourdata also lacks variation in SMS pricing making the estimates on price elasticity of SMS less credible. Ourmodel also employs specific functional forms for the utility structure and assumes distributional forms forvarious parameters. While many of these assumptions are widely used in literature, our results shouldbe interpreted appropriately.

Our current work is focused on Voice and SMS in mobile service. As we outline in the discussionsection, wireless operators are increasingly offering multiple applications and services. Future work shouldanalyze more prominent data services like WAP (Wireless Application Protocol) or application usage.Our model also ignores the network externalities. This would be another promising area to explore. Webelieve our paper takes a step in this direction and informs readers of the challenges of data in a complexsetting and the models needed to analyze such data to provide insights into this market.

7 Reference

Ahn, H. and M. Lee (1999), “An Econometric Analysis of the Demand for Access to Mobile TelephoneNetworks,” Information Economics and Policy, 11 (3), 297-305.

Albert, James H. and Siddhartha Chib (1993), “Bayesian Analysis of Binary and Polychotomous

30

Response Data,” Journal of the American Statistical Association, 88 (422), 669-679.

Andersson, Kjetil, Frode Steen, and Øystein Foros (2006), “Text and Voice: Complements, Substi-tutes or Both?” CEPR Discussion Paper No. 5780 Available at SSRN: http://ssrn.com/abstract=933111.

Burtless, G. and Jerry Hausman (1978), “The Effect of Taxation on Labor Supply: Evaluatingthe Gary Negative Income Tax Experiment,” Journal of Political Economy, 86, 1103-1130.

Chiang, J. (1991), “A Simultaneous Approach to the Whether, What and How Much to BuyQuestions,” Marketing Science, 10 , 297-315.

Chung, J. and V. R. Rao (2003), “A General Choice Model for Bundles with Multiple-CategoryProducts: Application to Market Segmentation and Optimal Pricing for Bundles,” Journal of MarketingResearch, 40 ), 115-130.

Danaher, P.J., B. Hardie, and W. Putsis (2001), “Marketing-mix Variables and the Diffusion ofSuccessive Generations of a Technological Innovation,” Journal of Marketing Research, 38 , 501-514.

Economides, Nicholas, Katja Seim, and V. Brian Viard (2008), “Quantifying the Benefits of Entryinto Local Phone Service,” RAND Journal of Economics, 39 (3), 699-730.

Enriquez, Luis, Stenfan Schmitgen, and George Sun (2007), “The true Value of Mobile Phones toDeveloping Markets,” The McKinsey Quarterly, September 17.

Garbacz, C. and H. G. Thompson (2007), “Demand for Telecommunication Services in DevelopingCountries,” Telecommunications Policy, 31 (5), 276-289.

Garbacz, C. and H. G. Thompson (2003), “Estimating Telephone Demand with State DecennialCensus Data from 1970-1990: Update with 2000 Data,” Journal of Regulatory Economics, 24, 373-378.

Gruber, H. (2001), “Competition and Innovation: The Diffusion of Mobile Telecommunications inCentral and Eastern Europe,” Information Economics and Policy, 13, 19-34.

Grzybowski, Lukasz and Pedro Pereira (2008), “The complementarity between calls and messagesin mobile telephony,” Information Economics and Policy, 20(3), 279-287

Hanemann, W. Michael (1984), “Discrete/continuous models of consumer demand,” Econometrica,52 , 541-561.

Hausman, J. (1999), “Cellular Telephone, New Products and the CPI,” Journal of Business andEconomic Statistics, 17, 188-194.

Iyengar, Raghuram (2004), “A Structural Demand Analysis for Wireless Services Under NonlinearPricing Schemes,” Working Paper.

Kling, J. P. and Van der Ploeg (1990), “Estimating Local Call Elasticities with a Model of Stochas-tic Class of Service and Usage Choice,” in Telecommunications Demand Modeling, A. de Fonteny andM. H. Shugard and D. S. Sibley, Eds. New York: North-Holland.

Krishnamurthi, Lakshman and S.P. Raj (1988), “A Model of Brand Choice and Purchase QuantityPrice Sensitivities,” Marketing Science, 7, 1-20.

31

Manchanda, P., A. Ansari, and S. Gupta (1999), “The Shopping Basket: A Model for Multicate-gory Purchase Incidence Decisions,” Marketing Science, 18, 95-114.

Miravete, E. and L. Roller (2004), “Estimating Markups under Nonlinear Pricing Competition,”Journal of the European Economic Association, 2, 526-535.

Miravete, Eugenio J. (2002), “Estimating Demand for Local Telephone Service with AsymmetricInformation and Optional Calling Plans,” The Review of Economic Studies, 69, 943-971.

Moffitt, Robert (1990), “The Econometrics of Kinked Budget Constraints,” Journal of EconomicPerspectives, 4 , 119-139.

Niraj, Rakesh, V. Padmanabhan, and P. B. Seetharaman (2005), “A cross-category model ofhouseholds’ incidence and quantity decisions,” Marketing Science, 27 (2), 225-235

Park, Rolla Edward, Bruce M. Wetzel, and Bridger M. Mitchell (1983), “Price Elasticities forLocal Telephone Calls,” Econometrica, 51 , 1699-1730.

Rodini, M., M. Ward, and G. Woroch (2003), “Going Mobile: Substitutability between Fixed andMobile Access,” Telecommunications Policy, 27 (5-6), 457-476.

Rossi, Peter E., Robert E. McCulloch, and Greg M. Allenby (1996), “The Value of PurchaseHistory Data in Target Marketing,” Marketing Science, 15 , 321-340.

Seetharaman, P.B., Siddhartha Chib, Andrew Ainslie, Peter Boatwright, Tat Chan, Sachin Gupta,Nitin Mehta, Vithala Rao, and Andrei Strijnev (2005), “Models of Multi-Category Choice Behavior,”Marketing Letters, 16 (3-4), 239-254.

Song, Inseong and P.K. Chintagunta (2007), “A Discrete/Continuous Model for Multi-CategoryBehavior of Households,” Journal of marketing research, 44 (4), 595-612

Sung, Nakil and Yonghun Lee (2002), “Substitution Between Mobile and Fixed Telephones inKorea,” Review of Industrial Organization, 20, 367-374.

Tammo, B., H. Van Heerde, R. Pieters (2005), “New empirical generalizations on the determinantsof price elasticity”, Journal of Marketing Research, 42 (2), 141-156.

Taylor, L. D. (1994), Telecommunication Demand in Theory and Practice, Springer, First edition.

Taylor, L.D. and D.J. Kridel (1990), “Residential Demand for Access to the Telephone Network,”in Telecommunications Demand Modeling, A. de Fonteny and M. H. Shugard and D. S. Sibley, Eds. NewYork: North Holland Publishing Co.

32